metastable copper chromium thin films

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Metastable copper-chromium alloy films

A: P. Payne and

B.

M. Clemens

Department of Materials Science and Engineering, Stanford University, Stanford, California 94305-2205

(Received 21 November 1991 ; accepted 18 February 1992)

Due to the large positive heat of mixing associated with the Cu-Cr binary system, solid

solutions exist only as nonequilibrium states. In this study, a series of metastable Cu-Cr

alloys ranging in composition from 14.1 to 75.4% copper was fabricated by sputter

deposition. Symm etric, asym metric, and grazing incidence x-ray diffraction geom etries

were used to trace the phase transition from bcc to fee crystal structures with increasing

Cu fraction. It is shown that the transition takes place not by a two-phase region

suggested by equilibrium thermodynamics, but rather through gradual disordering of the

bcc lattice as copper atoms are substitutionally accommodated. At a critical saturation

near 7 1 % Cu, the bcc structure beco mes unstable relative to the fee and a phase transition

occurs. The free energies of the kinetically constrained Cu-Cr system are modeled and

the results are found to agree well with observed behavior.

I. INTRODUCTION

A notable aspect of the copper-chromium phase

diagram is the strong chemical aversion between the

two elements. At room temperature, the solubility of

chromium in copper is limited to 0.02%, while that of

copper in chromium is believed to be even less.

1

The

elements are even immiscible in the liquid state, exhibit-

ing a miscibility gap that persists to an undetermined

temperature. Cu-Cr alloys are of technological interest

in applications ranging from electrical switches

2

to catal-

ysis. Study of Cu—Cr alloys over a wide composition

range is hindered, however, by the large positive heat of

mixing exhibited by the system.

Several efforts have been made toward extending

the solubility of chromium in copper. Rapid quenching

techniques such as splat cooling and melt spinning have

produced supersaturations as high as 1.8 .

3

Pulsed laser

irradiation has pushe d solubility as high as 4%.

4

Electron

and ion beam irradiation have also been employed with

limited success.

5

Each of the above techniques encoun-

ters difficulty in mitigating the liquid phase immiscibility

of the Cu-Cr system. In this regard, direct deposition

from the vapor phase has been shown to dramatically

increase solid solubility. Co-evaporation of copper and

chromium has previously been shown to restrict the

two-phase region to between 60 and 70% copper.

6

In

the present study it was found that sputter deposition

completely suppressed the formation of a two-phase

region, resulting in a continuous range of metastable

alloys.

II. FILM PREPARATION AND ANALYTICAL

TECHNIQUES

Cu-Cr alloy films were produced by co-deposition

of Cu and Cr onto two 3" stationary (100) silicon wafers

positioned between the magnetron sputter sources. The

base pressure of the system was 1 x 10"

7

Torr, while

sputtering was carried out in a 2.3 mT argon ambient

at a deposition rate of 6 A /s . The source-substrate

distance is 13 cm for normal incidence sputtering in this

system. Because the wafers were positioned between the

sources, however, the source substrate distance varied

from approxima tely 13 to 22 cm across the pair of

wafers. The path length difference induced a spatial

variation in flux from each source across the wafers,

resulting in a continuous range of compositions between

14.1 and 75.4% Cu. The wafers were cleaved into a total

of 27 segm ents, each 5 mm wide by 2 cm long . The

average composition of each slab was then determined

using an electron beam microprobe.

The use of several x-ray diffraction techniques en-

abled complete structural determination. The diffraction

geometries are shown in Fig. 1. Symmetric Bragg geom-

etry (SB), where the scattering vector (q) is parallel to

the surface normal, was used to measure crystallographic

structure of atomic planes parallel to the surface. Due

to texture in our samples, however, this technique is

able to access only a single reciprocal lattice point

and its higher harmonics. To investigate other plane

spacings, asymmetric Bragg geometry (AB), where q

forms an angle 10 to the surface norm al, was used to

measure atomic planes inclined at various angles to the

surface. Grazing incidence x-ray scattering (GIXS) was

used to measure lattice spacings for planes with normals

lying in the surface. Here q is nearly perpendicular to

the sample normal.

7

The combination of these three

techniques allowed us to track phases over a wide range

of compositions in the Cu-Cr system. In addition to the

x-ray techniques, high resolution transmission electron

microscopy was also used to study the structure of the

alloys.

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J. Mater. Res. Vo l. 7 No. 6 Jun 1992 1992 Materia ls Research Soc ie ty

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A

P. Payne and B. M. Clemens: Metastable copper-chromium alloy films

III.

RESULTS

A. Microprobe analysis

Results of the electron beam microprobe analysis in-

dicated a smooth and approximately linear concentration

gradient across the wafers, with compositions ranging

from 14.1 to 75.4 Cu. Composition variations within

each cleaved sample were determined to be less than

4

in all cases.

B Diffraction analysis

Symmetric Bragg diffraction revealed only one peak

and its higher harmonics for each of the compositions

studied, indicating a growth direction texture and sug-

gesting the presence of only a single phase at each

composition. Figure 2 shows a plot of growth direc-

tion J-spacing as a function of composition. On the

chromium-rich side, the ^-spacing was found to be

120-

(a) Symmetric Bragg

(b) Asymmetric Bragg

(c)

Grazing Incidence

FIG. 1. Scattering geometries used in this study. Collective imple-

mentation of the SB, AB, and GIXS geometries allows full structural

determination

in textured

films,

(a) Symmetric Bragg, (b) asymmetric

Bragg , and (c) grazing incidence.

1-2.09

Bulk Cr (110)-

2 04

20 30 40 50

Atomic Cu

60

70

FIG. 2. Growth direction rf-spacing (A), grain size (A), and peak

intensity (arbitrary linear scale) as function of Cu content (Cu K

o

radiation).

Note the rapid change in growth direction d-spacing, the

reduced grain size, and the diminished peak intensity in the region

between 50 and 70 Cu.

0.5 larger than the bulk value of 2.040 A for Cr(110).

With increasing Cu content, the ^-spacing exhibits a

gradual decrease up to roughly 53 Cu, at which point

it increases rapidly though continuously toward that of

Cu(lll) .

In addition to the rapid change in ^-spacing and

low intensity between 50 and 70 Cu, the peaks also

attain their greatest width in this region. This is shown

in Fig. 2 in which peak widths have been translated via

the Scherrer relation into average grain size in the growth

direction. Analysis of first and second order harmonics

indicated that finite size effects are the primary source of

broadening. The small grain size was confirmed in the

orthogonal direction (film plane) with high resolution

TEM, which revealed a nanocrystalline grain structure

in the alloys. Figure 3 shows a 20 A grain from a 60.5

Cu specimen. As Fig. 2 shows, the average grain size is

largest for the Cr-rich alloys but decreases to a minimum

in the transition region and rises again only slightly for

the Cu-rich alloys.

Figure 4 shows a series of GIXS measurements

taken for representative alloys. For the chromium-rich

alloys (top spectra), a well-developed bcc structure is

evident. As more copper is added to the bcc lattice,

however, the structure gradually disorders, as evidenced

both by broadening of the peaks and reduction of their

intensity. Between approximately 66 and 71 Cu, a

transition occurs from a disordered bcc structure to

a disordered fee structure. This is manifested by the

appearance of a broad Cu(220) peak in the lowermost

spectrum in Fig. 4, as well as by the movement of the

growth direction peak toward lower angles correspond-

ing to Cu(lll). A well-ordered fee phase was not evident

within the composition range studied.

J.

Mater. Res. Vol. 7 No. 6 Jun 1992

1371





A. P. Payne and B. M. Clemens: Metastable copper-chromium alloy films

FIG. 3. Planar HREM image of nanocrystalline grain structure in a

60.5%

Cu alloy. Though the grain size is not typical for this alloy,

the micrograph is intended to emphasize the nanocrystalline nature of

the metastable alloy.

Further characterization of the phase transition was

achieved with the asymmetric Bragg geometry. An offset

angle of 30° allowed both the Cu(311) and Cr(211)

peaks to be monitored simultaneously. These results are

combined with those from the SB and GIXS geometries

in Fig. 5 which shows the observed peaks as a function

of composition. White markers correspond to peaks

associated with bcc phase and the black with fee phase.

C. Effect of annealing

Figure 6 shows the result of vacuum-annealing a

60.5%

Cu alloy at 10 °C /m in to 500 °C. The sam ple

was subsequently allowed to cool to room temperature

inside the vacuum. The single peak splits into two which

correspond closely to bulk Cu(lll) and Cr(110). The

separation of these peaks is larger than the width of

the original peak, indicating our ability to distinguish

single-phase from dual-phase microstructures.

IV. DISCUSSION

A. Dilation of the bcc lattice

As mentioned previously, the chromium-rich alloys

exhibit a 0.5% dilation normal to the film plane relative

to the bulk Cr lattice parameter (2.885 A; see Fig. 2).

A similar expansion in the film plane was evident from

the GIXS spectra, suggesting that the expansion is not a

Poisson effect induced by in-plane compressive stresses.

Nor does the expansion appear to be a result of defects

induced during deposition since the lattice parameter of

pure chromium films was found to be within 0.1% of its

bulk value (2.888 A). Annealing of the alloys resulted

in a relaxation into two phases with lattice parameters

corresponding closely to bulk Cu and Cr. The anomalous

dilation thus appears to be a direct consequence of the

substitutional copper atoms present in the chromium-rich

lattice.

M l 10)

1

•

J

•i f

Cr(200)

\

to*

Cr(211) Cr(220)

1

SI

65

4.1%

«_

i .7

».7

Midi

Cu

C u

Cu

r

r

40

71.4 %Cu

50

I T; I I I

60 70 80 90 100

Two Theta' (Degrees)

Cu(l l l ) Cu(220)

FIG. 4. GIXS spectra for several alloys inc reasing in Cu con tent.

Note the systematic broadening and attenuation of bcc peaks and the

final appearance of a weak fee structure (As y n c h r o t r o n = 1-5094 A ).

For clarity, the intensity scale has been systematically expanded in

moving toward the copper-rich alloys.

Through the bulk modulus, the lattice dilation can

be related to the enthalpy of mixing AHm) for a single

phase.8 The qualitative result of such an analysis is that

positive heats of mixing lead to lattice dilations, whereas

negative heats of mixing lead to lattice contractions.

We performed such a calculation for the Cu-Cr system

by considering the molar change in volume associated

with a reversible, adiabatic lattice relaxation following

the introduction of Cu atoms into a Cr host lattice.

Using value for AHm derived from a mo del presented

in Sec. IV. D, this calculation correctly predicts a lattice

dilation, although its magnitude is overestimated. The

slight contraction of the lattice with increasing copper

content may be evidence of clustering among the cop-

per atoms. Though we present no direct evidence for

clustering, it is known that in A-B systems with large

positive heat of mixing, clustering can effectively reduce

1372

J. Mater. Res., Vol. 7, No. 6, Jun 1992





A. P. Payne and B. M. Clemen s: M etastable copper-chromium alloy films

o Cr(llO)

• Cu( l l l )

o Cr(200)

• Cu(220)

2.0 —

60

u 1-6-

en

Q

1.2 —

0.8

C8XCCCCQ000 O OOOOO

BCC

n Cr(211)

• Cu(311)

FC C

0

o o

man

an

D D D D D

10 20 30

40 50

60

70 80 90 100

Atomic

%

Cu

FIG. 5. Summary of all observed reflections and rf-spacings via SB,

AB , and GIXS geometries. Phase transition from bcc to fee structures

occurs near 7 1 % Cu. Light and dark shading indicates composition

regime of bcc and fee phases, respectively. White and dark markers

indicate observed bcc and fee reflections, respectively.

the number of A-B pairs from that in a conventional reg-

ular solution.

9

Thermodynamic models for this behavior

involve a reduction in the AH

m

and hence lattice dilation

which is most severe at the 50% composition: this trend

is observed in the data.

B. Texture of the bcc and fee phases

The symmetric Bragg spectra revealed only Cr(M0)

and Cu hhh) type reflections across the entire composi-

tion range studied, suggesting texturing of the close(est)

packed planes perpendicular to the growth direction.

This was confirmed by the in-plane GIXS measurements.

In this geometry, allowed reflections are determined

by both the usual structure factors as well as by the

requirement of a zero scalar product with the Miller

indices of the planes perpendicular to the growth di-

rection. All of the allowed reflections for bcc chromium

are evident in the GIXS spectra for the chromium-rich

alloy (top spectrum, Fig. 4). As the bcc lattice becomes

increasingly disordered, these peaks broaden and their

intensity wanes. For the most copper-rich alloy (bottom

spectrum, Fig. 4), a broad (220) peak appears, signaling

the evolution of a disordered fee phase. A C u ( ll l)

reflection is also evident in this spectrum, resulting from

mosaic spread in texture. Since conjugate (111) type

planes form an angle of 70.53°, misorientation of the

plane through 19.5° renders the peak accessible to the

GIXS geometry. Figure 7 shows the rocking curve from

the fee (111) phase of the 75.4% Cu alloy obtained in the

SB geometry. The FWHM of 16° confirms the mosaic

spread in the disordered fee phase.

C. X-ray visibility of second phases

The observation of only a single peak and its higher

orders in the SB diffraction geometry suggests that the

alloys are single phase. Further confirmation comes from

observation in other directions in reciprocal space where

the peak separations are greater. For example, in GIXS

geometry the Cr(200) and (220) peaks are separated by

several degrees from the Cu(2 20), as shown in Fig. 4,

where there is no indication of the presence of two

phases. A question nevertheless remains about the x-ray

S

0)

BulkCu(l l l ) -

Pre Anneal

Post Anneal

1 r

40

1

I '

42

Bulk C r (110)

i i r

44

46 48

Two Theta (Degrees)

FIG. 6 . Effect of vacuum annealing to 500 °C at 10 °C /m in and

subsequent cooling to room temperature. Note the bifurcation of the

growth direction peak into peaks corresponding closely to bulk Cu

and Cr.

1

10

1

15

1

20

Theta

1

25

(Degrees)

1

30

1

35

40

FIG. 7. Rocking curve on fee (111) for 75.4% Cu alloy, indicating

partial texturing of the fee Cu phase. The breadth of the peak

explains the presence of the technically forbidden Cu(lll) peak in

the lowermost GIXS spectrum shown in Fig. 4 .

J. Mater. Res. Vol. 7 No. 6 Jun 1992

1373





A. P. Payne and B M. Cleme ns: M etastable copp er-chromium alloy films

visibility

of a second phase, and we address this with a

simple volumetric argument. We estimate the intensity

and peak width of reflections from the hypothetical fee

Cu phase relative to those observed in the bec peaks,

and demonstrate that this leads to a contradiction with

the observed data.

Suppose the alloy is a two-phase mixture in which

one constituent (arbitrarily Cr) exists as a precipitate

in a matrix of the other. We idealize this hypothetical

microstructure as a simple cubic array of spherical bec

Cr precipitates of radius r^ and spacin g s in a fee Cu

matrix. W hile other arrays are possible, this one gives the

same order of magnitude results as other choices. The

assumption of spherical grains is not egregious, since

grain sizes for Cr-rich alloys measured perpendicular

and parallel to the film plane yielded dimensions of

120 and 90 A, respec tively (aspect ratio x, 0.75). We

assume that the coherence length of x-rays within the

copper matrix does not exceed the precipitate spacing 5.

While it may in fact exceed s, our assumption leads to

an overestimation in peak width which would degrade,

rather than enhance, peak visibility. Reversing the roles

of Cu and Cr as precipitate and matrix does not affect

the result of the calculation.

Since the prospect of a two-phase region is most

likely in the region between 60 and 70% Cu, the

65.7% Cu alloy is selected to test this. The bec peaks

from this alloy (Fig. 4) are fitted to gauss ian profiles

to determine their amplitude and width. These widths,

together with the alloy composition, are used to calculate

r

Cr

and 5 for the hypothetical microstructure. From these

dimensions, the widths of the fee Cu reflections are

estimated. The amplitude of the Cu reflections relative to

the observed Cr peaks are calculated according to atomic

fraction, structure factor, scattering factor, and in-plane

multiplicity for the particular Cu reflection. The result of

the calculation for the hypothetical fee Cu(220) reflection

is shown in Fig. 8. The Cu(220) reflection is predicted to

be much more intense than those of the neighboring bec

Cr peaks, in contradiction with the data. The calculation

also predicts that, if present, crystalline clusters of fee

Cu as small as 11 A in diameter would produce a (220)

reflection of equal amplitude and comparable width to

the observed Cr(220) peak. We interpret this as further

evidence for the single phase nature of the alloys.

D. Thermodynamics aspects of relative

phase stability

Experimentally, we find the bec phase to dominate

over nearly the entire composition range studied. It is

noteworthy that an alloy of roughly 70% Cu adopts the

bec structure of chromium. A theoretical basis for this

finding is afforded by simple thermodynamic concepts.

The free energy (g) vs composition x) curves for each

60

Two Theta (degrees)

FIG. 8. Observe d in-plane structure (circles) and hypo thetical Cu(2 20)

reflection predicted by two-phase model (line) for a 65.4% Cu alloy.

The intense Cu peak predicted by the model is not evident in the data,

indicating a single phase bec structure despite the high concentration

of copper.

of the phases can be modeled to determine their relative

stability. This is carried out by first determining the

endpoints for the

g-x

curves. The free energies of the

pure constituents in their naturally occurring phases are

known, while the free energy difference between the bec

and fee structures of each of the pure constituents can be

estimated using the lattice stability parameters developed

by Kaufman.

10

Enthalpy of mixing is determined using

the Miedema model,

11

and the entropy of mixing is

calculated after an ideal solution model.

The results of these calculations for the Cu-Cr

system at 300 K are presented in Fig. 9. The stable

phases at this temperature are determined by constructing

the common tangent between the lowest curves. In this

case this would indicate nearly pure Cu and Cr to be the

stable phases, in agreement with the equilibrium phase

diagram. The resulting metastable phases, however, are

determined by accessing the lowest free energy curve

at a particular com position. Figu re 9 shows that the

metastable bec phase is favored over all others up to

roughly 78% Cu. Experimentally, the bec phase was

found to dom inate up to roughly 7 1 % Cu (Fig. 5). The

discrepancy probably results from inaccuracies in the

estimated lattice stabilities. These parameters essentially

determine the vertical positions of the curves; since

the bec and fee

g-x

curves are nearly horizontal near

their point of intersection, small vertical displacements

of the curves can lead to large horizontal variations in

their point of intersection. Despite this, the experimental

results agree remarkably well with those of the model.

One important aspect of these results is that they are

specific to the growth conditions. How wel l the Cu -C r

1374

J.

Mater. Res. Vol. 7 No. 6 Jun 1992





A. P. Payne and B. M. Cleme ns: M etastable copper-chromium alloy films

BCC

0.0

T

0.2 0.4 0.6

Atom ic Fraction Cu

FIG. 9. Calculated g-x diagram for several phases of the Cu-Cr

system. For a completely kinetically constrained system, the calcu-

lation predicts an abrupt transition from bcc to fee structures around

78 % Cu, in reasonable agreement with experiment (7 1% Cu).

system follows the behavior described by the above

model depends largely on the kinetics of deposition;

fabrication techniques approaching equilibrium growth

conditions obviously would not lead to metastable final

products. Perhaps this explains the existence of the

two-phase region described by other researchers.

6

Ther-

malization of sputtered atoms often results in arrival en-

ergies less than those by evaporation techniques.

12

These

factors would be expected to foster highly nonequilib-

rium growth conditions at the film surface. In light of

the excellent agreement of the observed behavior with

the model, this indeed seems to be the case; sputter

deposition is quite effective in completely preventing the

growth of the thermodynamically stable products.

V. CONCLUSIONS

A. Single phase solid solution

Although a two-phase field between 60 and 70% Cu

was described in earlier studies on metastable Cu-Cr

alloys,

6

no evidence of such a region was found in

this study; we maintain that under appropriate sputter-

ing conditions the two-phase region can be completely

suppressed. The evidence for this conclusion is summa-

rized below.

(1) Though a two-phase region will exhibit peaks

from both structures, nowhere in Fig. 5 are the bcc and

fee phases observed to coexist. While it is conceivable

that one of the constituents be dispersed on such a fine

scale that it is rendered indiscernible with x-rays, we

have presented arguments to the contrary.

(2) The growth direction ^-spacing exhibits no dis-

continuities. A two-phase region would necessarily show

a discontinuity in the lattice parameter since by definition

each phase can adopt only one of the two values.

Figure 2 shows, however, that the ^-spacing varies con-

tinuously, indicative of a single phase solid solution.

(3) Annealing leads to a distinct bifurcation of the

growth direction Brag g peak (Fig. 6) and relaxation

toward Cr(110) and Cu(110) d-spacings. This is the

expected behavior of a metastable single phase supplied

with sufficient activation energy for phase separation.

Arguments suggesting that this is strictly a result of

grain coarsening are addressed with the same concepts

presented in Sec. IV. C of the discussion.

B. The bcc/fcc transition via disordering

The transition from bcc to fee structures with in-

creasing copper content apparently does not occur by

the relative growth and diminution of components in a

two-phase field. We maintain that it occurs through the

gradual disordering of the bcc chromium lattice as an

increasing number of copper atoms are substitutionally

accommodated. At some critical saturation, the bcc lat-

tice becomes unstable relative to the fee and the alloy

adopts this structure. Evidence for these conclusions is

summarized below.

(1) The breadth and intensity of crystalline peaks

are direct measures of the extent of crystalline order in

a solid. Both the symmetric Bragg and the GIXS spectra

clearly depict the gradual broadening and weakening of

the bcc peaks with increasing Cu fraction. Beyond the

transition region, a broad, weak fee peak emerges.

(2) The reduced grain size in the transition region

(Fig. 2) is com men surate w ith a disordered structure.

Since the relative energy cost associated with grain

boundary surface is less for a disordered phase than for

an ordered one, the disordered phase is able to support

a larger ratio of interfacial area to grain volume, as

manifested in reduced grain size.

(3) For a kinetically constrained binary system, the

relative stability of one phase over the other changes

abruptly at a critical concentration. Both the mode of the

bcc to fee transition and the Cu concentration at which

it occurs are in excellent agreement with the kinetically

constrained thermodynamic model.

ACKNOWLEDGMENTS

We would like to thank Y.T. Chang at General

Motors Research Labs for his efforts in motivating this

study. We would also like to thank Rick Waldo, also

at GMR, for his assistance with the microprobe work.

We would like to acknowledge the Hertz Foundation

for its support of on e of us (A. P.). Finally, we wo uld

like to thank Sean Brennan at the Stanford Synchrotron

Radiation Laboratory for his help in carrying out the

GIXS experiments.

R F R N S

1. M. Hansen, Constitution of Binary Alloys, 2nd ed. (McGraw-Hill ,

New York, 1958).

J. Mater. Res. Vol. 7 No. 6 Jun 1992

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3.

G. Falkenh agen and W. Hofmann , Z. Metallkd . 43 , 69 (1952 ). 8. R.A . Swalin, Thermodynamics of Solids, 2nd ed. (John Wiley,

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Vanden berg, and A . G. Cu llis, in Laser and Electron Beam 11 . A. R. Miede ma, Philips Tech. Rev. 8, 36 (1976 ).

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metastable copper chromium thin films

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